Modeling a search space

data structure for state
	- immutable! (const) (usually)

data structure/model type for action
	- actions are how you get from one state to another

valid-moves: state -> list<action>

next-state: state x action -> state
	    (state,action) -> state
	"transition model"

eval-state: state -> ???
	bool   (accept / not)
	enum   (win / lose / draw / not-done)
	int  (score)

init-state: () -> state



in A* 262 project:

state: Location

action: 
	- N, S, E, W
	- or, just Location


Amsterdam to Prague train trip
w/ few transfers and doesn't take forever
(--> covers the shortest physical distance?)

state: city (i.e. the station that is in that city)
action: (city, city) (source and destination of one train route)

valid-moves: state -> list<action>
	list of connected cities (train routes that exit source city)

next-state: state x action -> state
	simply produces the "destination city" from that action

init-state: () -> state
	Amsterdam!

eval-state: state -> bool
	Is the city Prague?

heuristic: state -> score
	**Is this city adjacent to Prague? -> 0, 1, 2
	**What is the crow-flies distance from this city to Prague?



Prove (cos(x+y))/(cos x cos y)  === 1 - (tan x tan y)

state: an equation of two trigonometric expressions
action: a trig identity to apply

valid-moves:
	which trig identities match some part of the state?
next-state: state x action -> state
	apply the trig identity (action) to the current equation
	(state), produce new valid equation (state)
init-state:
	(cos(x+y))/(cos x cos y)  === 1 - (tan x tan y)
	
eval-state:
	Are both sides of the === exactly the same?


We have a sudoku starting board; solve it

state: the current board: 2d array of int (1-9, 0 for blank) [9][9]
action: (int num-to-place, pair(int x, int y))

valid-moves: 
	list of (number, position) pairs we could place
next-state:
	board after placing that number
init-state:
	initial board w/ pre-filled numbers
eval-state:
	is the board solved---is every space filled?